Expert: Robi Bhattacharjee - 9/21/2008

Question
QUESTION: If p is an integer and 3 is the remainder when 2p+7 is divided by 5, then what value is p?

I got 4 and i doubled check and fits the formula. But the correct answer is 3.

ANSWER: Hello Emily,

For these kinds of problems, it helps to use an equation.

So 2p + 7 is congruent to 3 mod(5).

In equations like this, you can do both sides to the equation, but when you are done, you have to put things into their remainder when divided by 5. So 6 becomes 1 since 6 = 1 + 5.

Now 2p + 7 = 3

so 2p = -4

so p = -2.

So when you add a five to negative two, you get

p = -2 + 5.      Remember that in these kinds of equations, you can add whatever the mod is to one side or the other side as much as you want.

p = 3.

Lets try it out. 2(3) + 7 = 13. This has a remainder of 3 when divided by 5 since 13 = 2*5 + 3.

Now lets try 4 out. 2(4) + 7 = 8 + 7 = 15 which is divisible by 5, so it doesn't have a remainder of 3. This means that it doesn't work.


So the answer is p = 3.


I hope this helped,
Robi

---------- FOLLOW-UP ----------

QUESTION: I still don't quite get it. Doesn't it say that 2p+7 divided by 5? Then how can it still be p=-2+5? I really suck at these word problems.
Thanks in advance

Answer
Hello Emily,

It said that when 2p + 7 is divided by 5, it leaves a remainder of 3. This means that it will basically have 3 leftover after being divided by 5. So that is what it meant.







I hope this helped,

please ask If you still aren't clear,



Robi